On Jun 8, 2:49 pm, Robert Heller wrote:
At Mon, 8 Jun 2009 14:40:47 EDT "Ken S. Tucker" wrote:

On Jun 7, 6:56 pm, dotcom wrote:
I thought I understood basic gravity problems but the following high
school physics problem from my daughter has me stumped ( I think)
Q. a disabled ( meaning of disable not defined) satellite of mass
2400kg is in orbit at a ht of 2000 km above the earth at a speed of
6900 m/s. ( my calc show that is exaclty the speed required for a
circular orbit at that ht). it then says the satelite falls to a ht
of 800 km calculate what the new speed at the lower ht..
well I simply calculated the gain in potential energy ( PE = delta
GMm/r) and equated this to the gain in kinetic energy ( =0.5 mv^2)
as the satellite must speed up. and added this to the original speed
of 6900 m/s to get 10870 m/s , but I am not sure that this correct.
it certainly doesnt give me the answer in the school text book of 7900
m/s

( I used G=6.67E-11, M =5.98E24 kg and r= 6.38E6 m.
using this the loss in potential energy = 1.9E10 J

I suspect I am going wrong somewhere in not accounting for the fact
velocity is a vector quantitiy. Surely it must depend on the direction
the satellite is heading initally. is this really a solvable problem?

It's ok, some specific info is lacking.
How does a disabled satellite retro fire?
((BS baffles brains))
It sounds like you are expected to find the orbital
velocity at 800km when an impulse was applied to
the sat at 2000 km, to retro fire into an elliptical
orbit with perigee at 800 then retro fire again to
circularize. Anyway assuming you had help from
pink fairies, the standard circular orbit equation is,
Vo = sqrt( GM/r ) .
Ken

I have a question (knowing practically zip about orbital machanics). If
the satellite was passively in its 2000 km orbit would this orbit
(eventually) decay (friction from cosmic dust or something)? Maybe the
high school program is thinking of this sort of situation. In this case
the 'pink fairies' would just be an entropy effect.

Here's a ref on circular orbital speed,
http://ceres.hsc.edu/homepages/class...ics/sec10.html
and I'll suggest an examination of lunar recession,
http://www.astronomy.ohio-state.edu/...it4/tides.html
Those are .edu sites and look good to me. The latter shows
that the Moon is receeding from the Earth.

Ok, orbital decay of a 2000 km orbiting sat is nearly
impossible to predict, (IMHO), because there are many
tiny effects (sometimes called perturbations) to be
considered. One would even have to know the shape and
material of the satellite and specific orbit, to calculate
atmospheric drag, magnetic field effects, solar wind,
effect of the moon and so forth.
Regards
Ken